1. Field of the Invention
The present invention relates to phase matching in high harmonic generation (HHG) using a non-collinear pulse to modulate the field seen by the driving pulse. In particular, the present invention relates to such phase matching using a weak, long duration non-collinear modulation pulse intersecting the driving pulse.
2. Description of the Prior Art
High-order harmonic generation (HHG) driven by ultrashort laser pulses is a source of extreme-ultraviolet and soft X-ray light with the unique properties of ultrashort pulse duration and high spatial and temporal coherence. This source has made possible new ultrafast spectroscopic probes of atoms, molecules and materials. So far, however, most applications have used relatively long wavelengths, because the conversion rapidly decreases at shorter wavelengths. This decrease is not due primarily to the very high-order nonlinearity of the process—in fact, the atomic physics of HHG is non-perturbative, and has favorable scaling to shorter wavelengths. The major challenge is that, unlike low-order nonlinear processes such as second-harmonic generation, HHG is inherently associated with ionization of the nonlinear medium. In HHG, an electron is first ionized by the field of an intense femtosecond laser. Once free, the electron begins to oscillate in response to the laser field. A small fraction of the ionized electron can re-collide with its parent ion, recombining and liberating the excess energy as a short-wavelength photon.
As in all nonlinear parametric processes in nature, efficient conversion of light from one frequency to another using nonlinear optics requires that the process be phase-matched. As the pump beam propagates, the nonlinear response of the medium coherently adds to the harmonic signal. The generated field continues to add constructively if the two waves travel with the same phase velocity through the medium, leading to a bright, phase-matched beam at the new wavelength. If the process is not phase-matched, coherent build-up is limited to a propagation distance over which the relative phase of the fundamental and the harmonic light slip by 180°. This distance is the coherence length Lc=π/Δk, where Δk is the phase mismatch between the polarization wave and the harmonic wave. For HHG, dispersion of the free-electron plasma reduces Lc to the micrometer or even sub-micrometer range for up-conversion to very short wavelengths, which are only generated when the laser is very intense and thus the medium is already highly ionized. As a result, efficient harmonic generation is possible only at relatively low levels of ionization, below a ‘critical’ ionization level of around 5% for Argon or around 0.5% for helium, corresponding to photon energies of around 50 eV and around 130 eV respectively. Thus, new methods that can correct for this phase mismatch in ionized media (plasmas) are a ‘grand challenge’ in this area of laser science.
In the absence of phase-matching, quasi-phase matching (QPM) techniques have been successfully demonstrated to compensate for this phase slip by periodically readjusting the relative phase of the fundamental and nonlinear response at an interval corresponding to the coherence length. In the visible region, this is achieved by periodically reversing the polarization of a non-centrosymmetric nonlinear-optical material. However, this implementation cannot be used for HHG, because HHG uses a low-pressure gas as the nonlinear medium.
Past experimental work used a periodically modulated hollow waveguide to modulate the intensity of the driving laser to implement QPM for high-harmonic generation. U.S. Pat. No. 6,151,115, incorporated herein by reference, is a useful background reference. Even a small modulation (around 1%) of the driving laser results in significant modulation in both the amplitude and phase of the harmonics. Although this past work succeeded in enhancing conversion efficiency into the soft X-ray region of the spectrum by about one order of magnitude, further optimization will require a more sophisticated approach. This is because optical loss of the driving laser, refraction, mode beating and group-velocity dispersion all result in a continuous variation of the coherence length along the direction of propagation, making it difficult to optimize the modulation period. Finally, modulation periods shorter than the waveguide diameter will not significantly influence the laser field, making it challenging to compensate for very short coherence lengths.
Recently, Voronov et al. demonstrated that a weak counterpropagating pulse can be used to disrupt high-harmonic emission, with the objective of using this technique to implement QPM. This experiment used a simple focused-beam geometry in a low-pressure gas. The counterpropagating field induced both a standing amplitude and phase modulation on the driving laser field. Even though the counterpropagating field was weak, it distorted the field of the driving laser, essentially turning off phase-coherent high-harmonic production in the region where the two pulses overlapped. That work also demonstrated that if the HHG signal is deliberately suppressed by a non-optimum focusing geometry, a single counterpropagating pulse can recover much of the original harmonic signal that had previously been obtained in the optimum-focus geometry. However, this work only investigated harmonic emission in regimes where conventional phase-matching was already possible in the medium. Attempts to obtain enhancements significantly greater than what could otherwise be obtained were not successful.
A pending U.S. patent application having some co-inventors with the present application teaches a technique for quasi-phase matching and quantum control of high harmonic generation in waveguides using a train of counterpropagating pulses. The counterpropagating pulse technique presents an advantage over previous QPM techniques in that varying the format of the counterpropagating light pulse allows for dynamic optimization of quasi-phase matching, and also because when short counterpropagating light pulses are used, shorter coherence lengths can be compensated for compared with using a structured waveguide. In this QPM technique, the counterpropagating pulses intersect with the driving pulse and suppress the HHG emission from out-of-phase regions. However, our calculations showed (OL 32, 2975) that the QPM efficiency factor in this technique is smaller than 0.15 (the QPM efficiency factor is the ratio between the generated signal under QPM and the generated signal under perfect phase matching condition). Thus, a need remains to devise a QPM method for HHG with larger QPM efficiency factor. In addition, the counterpropagating pulses QPM technique is limited to the case where the coherence length is larger than ˜10-100 microns. At keV energies, however, the coherence length is typically in the micron range.
A need remains in the art for a method of phase matching high harmonic generation (HHG) using one or more non-collinear modulating pulses intersecting the driving pulse that can be implemented using light pulses with duration >Lc, and that allows for a maximum QPM efficiency factor.